Coupled model of rotary-tilting spindle head for pose-dependent prediction of dynamics

Five-axis machine with rotary-tilting spindle head (RTSH) is always used for sculptured surface machining, and the tool-tip dynamics in various machining postures along the tool path directly affect the machining accuracy and stability. To rapidly evaluate the tool-tip dynamics at different postures during the structural design of tool-spindle-spindle head (TSSH) assembly, this paper proposes a coupled dynamic model of tool-spindle-bearing system (TSBS) and RTSH. The model is a rigid-flexible multibody dynamic model with 36 degrees-of-freedom (DOFs), where in the rotary shaft, swivel shaft and housing are treated as rigid bodies; the tool, tool holder, and spindle shaft are modeled by reduced beams; the bearings and flexible joints are modeled as spring-damping elements. The fully Cartesian coordinates and Lagrangian method are employed to deduce a general parametric dynamic equation. The analytical method for calculating the contact stiffness of bearings and flexible joints is systematically presented, including tool-holder joint, holder-spindle joint, spindle bearings, hirth coupling, and the bearings and locking joints of rotary and swivel shafts. The model is verified by the frequency response functions (FRFs) testing and modal testing at different postures. The experimental results show that the proposed model can be used for accurate and efficient evaluation of the tool-tip FRFs, natural frequencies and mode shapes of TSSH at an arbitrary posture.